# Informal Proof: Circumference of a Circle

Author:
KatGeog
Topic:
Circle
To find the circumference of a circle you can use the formula, C=.

## Find the circumference using the formula.

What is the circumference of a circle with a radius of 1 cm?

Select all that apply
• A
• B
• C

What is the circumference of a circle that has a radius of 10 in?

Select all that apply
• A
• B
• C

## Compare to the perimeter of a regular polygon inscribed in a circle.

In an earlier section, we found the perimeter of a regular polygon. We will use the perimeter of a regular polygon to estimate the circumference of a circle. On your paper, find the circumference of a circle that has a radius of 6 cm. Label this value, ACTUAL CIRCUMFERENCE. Use the slider to change the number of sides in the inscribed polygon. Start with 3 sides, then 4 sides, then 5 sides etc. Compare the perimeter of the n-gon to the circumference of the circle.

## Question

Move the slider and compare the actual circumference to the perimeter of the polygon. Explain what happens as you increase the number of sides on the polygon.

## Question

Do you think that the perimeter of the inscribed regular n-gon is a good estimate for the circumference of the circle? Why or why not?